Acoustics of a Viscoelastic Liquid with Perfluorocarbon Droplets in the Presence of Phase Transitions

• Published in: Lobachevskii journal of mathematics 2024-05, Vol.45 (5), p.1988-1996
• Main Authors: Gubaidullin, D. A., Gubaidullina, D. D., Fedorov, Yu. V.
• Format: Article
• Language: English
• Subjects: Acoustic attenuation; Acoustic waves; Acoustics; Algebra; Analysis; Attenuation coefficients; Droplets; Geometry; Liquid phases; Mass transfer; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Modulus of elasticity; Oscillations; Perfluorocarbons; Phase transitions; Phase velocity; Polydimethylsiloxane; Probability Theory and Stochastic Processes; Relaxation time; Rheological properties; Shear modulus; Storage modulus; Vapors; Viscoelastic liquids; Viscoelasticity; Wave attenuation; Wave dispersion; Wave equations
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224602169

In this work, a modified Rayleigh–Lamb equation which takes into account the radial oscillations of a perfluorocarbon droplet with a vapor bubble in the center in a viscoelastic liquid has been derived. The viscoelasticity of the carrier medium has been taken into account based on the Zener rheological model. For small inclusion oscillations, the problem of heat and mass transfer between vapor, liquid phase and carrier liquid has been solved. The energy equation has been found. Based on the obtained equations of radial oscillations of the inclusion, energy and the well-known wave equation for a bubbly liquid, the dispersion relation has been determined. For a mixture of polydimethylsiloxane with droplets of octafluoropropane C F and vapor bubbles in the center, the dependencies of the phase velocity and attenuation coefficient on the perturbation frequency have been plotted. The influence of the shear modulus and relaxation time of the elastic carrier liquid on the dynamics of acoustic waves has been illustrated.